Galileo's Paradox
in [Math]
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From: Virgil on 12 Dec 2006 16:10 In article <457EC403.80502(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 12/11/2006 10:35 PM, Virgil wrote: > > > Given any rational, it is easy to construct the set of all larger > > rationals, > > Really? Who gives me all rationals? ZFC and NBG, for starters.
From: MoeBlee on 12 Dec 2006 16:12 Tony Orlow wrote: > whereas Robinson makes sense and comes to all the right > conclusions. I kind of like that. :) Then you think that ZFC comes to all the right conclusions. MoeBlee
From: Virgil on 12 Dec 2006 16:15 In article <457EC740.4040606(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 12/11/2006 10:43 PM, Virgil wrote: > > In article <457D846A.3080208(a)et.uni-magdeburg.de>, > > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > > >> Cantor himself has shown with DA2 that they are not such field. > > > > False! EB apparently has no idea what DA2 says. > > What part of DA2 does EB allege shows that the reals are "not a complete > > ordered field"? > > If there is a number outside then the field is not complete. Does EB know of any numbers "outside"? If one is considering, say, the Dedekind construction, it has been shown that repeating the process does not create any new numbers. So where is this mythical "outside" to get its numbers from?
From: MoeBlee on 12 Dec 2006 16:15 Tony Orlow wrote: > Huh! Pfff!!! Tsss!! Just read the damn Robinson book as well as whatever you need for the required rudiments in mathematical logic and set theoery that are assumed that the reader undersands before even OPENING Robinson's book. MoeBlee
From: MoeBlee on 12 Dec 2006 16:19
Eckard Blumschein wrote: > Uncountable is the opposite of countable. Therefore it has also to > include non-sets. Oy vey. Blumschein POSSIBLY qualifies as even more hopeless than Orlow. MoeBlee |